Do international car rental companies like avis, thrifty etc. have franchise system or do they have their own fleet in each country/city/location?
Most major international car rental companies use a mix of franchise and corporate owned locations. For example, Thrifty (itself part of Hertz) has 340 corporate locations and over 1,020 franchise locations.
Franchise information is available on each rental company's website, and a search for "car rental franchise" will provide more information, including articles for and by franchise owners.